Geometric Methods in Degree Theory for Equivariant Maps [electronic resource] / by Alexander Kushkuley, Zalman Balanov.

Fundamental domains and extension of equivariant maps -- Degree theory for equivariant maps of finite-dimensional manifolds: Topological actions -- Degree theory for equivariant maps of finite-dimensional manifolds: Smooth actions -- A winding number of equivariant vector fields in infinite dimensional banach spaces -- Some applications.

The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations. The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non-linear analysis and representation theory.